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In this paper, we prove some existence results of solutions for a class of nonlocal initial value problem for nonlinear fractional hybrid implicit differential equations under generalized Hilfer fractional derivative. The result is based on a fixed point theorem on Banach algebras. Further, examples are provided to illustrate our results.

In this paper, we establish the existence and uniqueness of solutions for a class of initial value problem for nonlinear implicit fractional differential equations with Riemann-Liouville fractional derivative, also, the stability of this class of problem. The arguments are based upon the Banach contraction principle and Schaefer’s fixed point theorem. An example is included to show the applicability of our results.

In this paper the authors prove the existence as well as approximations of the solutions for the Bagley-Torvik equation admitting only the existence of a lower (coupled lower and upper) solution. Our results rely on an appropriate fixed point theorem in partially ordered normed linear spaces. Illustrative examples are included to demonstrate the validity and applicability of our technique.

We develop the existence theory for sequential fractional differential equations involving Liouville-Caputo fractional derivative equipped with anti-periodic type (non-separated) and nonlocal integral boundary conditions. Several existence criteria depending on the nonlinearity involved in the problems are presented by means of a variety of tools of the fixed point theory. The applicability of the results is shown with the aid of examples. Our results are not only new in the given configuration but also yield some new special cases for specific choices of parameters involved in the problems.

This manuscript is devoted to prove existence and stability results of random impulsive stochastic fractional differential equations(ISFDE's). Initially, a system is developed and the existence results of mild solutions are obtained using Banach Contraction Principle. By the use of Stochastic analysis techniques and sufficient conditions the results are formulated. Then. using continuous dependency of solutions on initial conditions, we establish the stability results. Finally, to demonstrate our results, an example is provided. [ABSTRACT FROM AUTHOR]

In this paper, we present new definitions of generalized fractional integrals and derivatives with respect to another function and derive some of their properties, such as their inter-relationship and semigroup law. Caputo-type generalized fractional derivative with respect to another function is also defined and its properties are derived. A Cauchy problem involving the new Caputo-type generalized fractional derivative is also studied. We also provide an expansion formula for Caputo-type derivative and apply it to solve a fractional-order problem. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence, uniqueness and stability results for a class of nonlinear impulsive Hilfer-Katugampola problems. Our reasoning is founded on the Banach contraction principle and Krasnoselskii's fixed point theorem. In addition, an example is provided to demonstrate the effectiveness of the main results. [ABSTRACT FROM AUTHOR]

We consider the solvability of fractional differential equations involving the Riesz fractional derivative. Our approach basically relies on the reduction of the problem considered to the equivalent nonlinear mixed Volterra and Cauchy‐type singular integral equation and on the theory of fractional calculus. By establishing a compactness property of the Riemann–Liouville fractional integral operator on Lebesgue spaces and using the well‐known Krasnoselskii's fixed point theorem, an existence of at least one solution is gleaned. An example is finally included to show the applicability of the theory. [ABSTRACT FROM AUTHOR]

In this article, we study the existence of solutions and their stability of random impulsive stochastic functional differential equations (ISFDEs) driven by Poisson jumps with finite delays. Initially, we prove the existence of the mild solutions to the equations by using Banach fixed point theorem. Then, we study the stability of random ISFDEs through the continuous dependence of solutions on initial condition. Next, we investigate the Hyers Ulam stability results under the Lipschitz condition on a bounded and closed interval. Finally, an example is presented to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence and uniqueness of solutions to boundary value problem for differential equations with generalized Hilfer type fractional derivative. The arguments are based upon the Banach contraction principle and Krasnoselskii's fixed point theorem. An example is included to show the applicability of our results. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the existence and uniqueness of solutions of a coupled system of nonlinear implicit fractional differential equations of Caputo-type modification of the Erdélyi-Kober involving both retarded and advanced arguments. The arguments are based upon the Banach contraction principle and Schauder's fixed point theorem. An example is included to show the applicability of our outcomes. [ABSTRACT FROM AUTHOR]

The Basset–Boussinesq–Oseen equation (BBO equation) is the mathematical formulation of the Lagrangian acceleration of a spherical particle, moving with Lagragian velocity, in an unsteady flow as the sum of the viscous, gravitational, buoyancy, virtual mass, and Basset forces acting respectively on the particle. Despite the widespread use of the equation in applications, the basic properties of its solutions have remained unexplored. Here we fill this gap by proving global existence and uniqueness of solutions in an appropriate partially ordered Banach space. The method also gives an approximate solution to the problem with accurate result which is easy to implement. Meanwhile, regularity properties of the solutions are proved under some conditions which gives a representation of the solutions. Illustrative examples exhibit the efficiency of our method. [ABSTRACT FROM AUTHOR]

In this paper, by using the fixed point theory and the technique relying on the concept of measure of noncompactness in Fréchet spaces, we prove some existence and Ulam-Hyers-Rassias stability results for some Hilfer and Hilfer-Hadamard fractional differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we establish suffcient conditions for the existence and stability of solutions for a class of nonlocal initial value problems for differential equations with Hilfer's fractional derivative, The arguments are based upon the Banach contraction principle. Two examples are included to show the applicability of our results. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence and uniqueness of solutions for a class of anti-periodic boundary value problem for nonlinear implicit fractional differential equations with impulse and Caputo fractional derivative. The arguments are based upon the Banach contraction principle, and Schaefer's fixed point theorem. An example is included to show the applicability of our results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of solution for boundary value problem with fractional differential equations with nonlocal conditions involving the standard Riemann-Liouville fractional derivative of order r ∈ (1; 2]. [ABSTRACT FROM AUTHOR]

We discuss the existence of solutions for a differential equation of fractional order with multi-point nonlocal boundary conditions via standard tools of fixed point theory. The paper concludes with some illustrative examples. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies a nonlinear three-point boundary value problem of sequential fractional differential equations of order with . The expression for Green’s function of the associated problem involving the classical gamma function and the generalized incomplete gamma function is obtained. Some existence results are obtained by means of Banach’s contraction mapping principle and Krasnoselskii’s fixed point theorem. An illustrative example is also presented. Existence results for a three-point third-order nonlocal boundary value problem of nonlinear ordinary differential equations follow as a special case of our results. [Copyright &y& Elsevier]

Abstract: This paper studies a nonlinear Langevin equation involving two fractional orders and with three-point boundary conditions. The contraction mapping principle and Krasnoselskii’s fixed point theorem are applied to prove the existence of solutions for the problem. The existence results for a three-point third-order nonlocal boundary value problem of nonlinear ordinary differential equations follow as a special case of our results. Some illustrative examples are also discussed. [Copyright &y& Elsevier]

Abstract: We study a class of anti-periodic boundary value problems of fractional differential equations. Some existence and uniqueness results are obtained by applying some standard fixed point principles. Several examples are given to illustrate the results. [Copyright &y& Elsevier]

Abstract: In this paper, we study the existence of solutions for nonlinear fractional differential equations and inclusions of order with families of mixed and closed boundary conditions. In case of inclusion problems, the existence results are established for convex as well as nonconvex multivalued maps. Our results are based on Leray–Schauder degree theory, nonlinear alternative of Leray–Schauder type, and some fixed point theorems for multivalued maps. Some interesting special cases are also discussed. [Copyright &y& Elsevier]

In this paper, we apply Bohnenblust- Karlins fixed point theorem to prove the existence of solutions for a class of higher order fractional differential inclusions with nonlocal boundary conditions. Some applications of the main result are also presented. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies a coupled system of nonlinear fractional differential equations with three-point boundary conditions. Applying the Schauder fixed point theorem, an existence result is proved for the following system where satisfy certain conditions. [Copyright &y& Elsevier]

In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions of first and second order periodic boundary value problems and periodic solutions of functional differential equations. We obtain some new results relative to the lower solution α and upper solution β with α⩽β. [Copyright &y& Elsevier]

We consider the nonlinear fractional Langevin equation involving two fractional orders with initial conditions. Using some basic properties of Prabhakar integral operator, we find an equivalent Volterra integral equation with two parameter Mittag–Leffler function in the kernel to the mentioned equation. We used the contraction mapping theorem and Weissinger's fixed point theorem to obtain existence and uniqueness of global solution in the spaces of Lebesgue integrable functions. The new representation formula of the general solution helps us to find the fixed point problem associated with the fractional Langevin equation which its contractivity constant is independent of the friction coefficient. Two examples are discussed to illustrate the feasibility of the main theorems. [ABSTRACT FROM AUTHOR]

We present in this work the existence results and uniqueness of solutions for a class of boundary value problems of terminal type for fractional differential equations with the Hilfer–Katugampola fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Banach contraction principle and Krasnoselskii's fixed point theorem. We illustrate our main findings, with a particular case example included to show the applicability of our outcomes. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence and uniqueness of solutions for a nonlinear fractional-order coupled system involving Caputo fractional derivatives of different orders equipped with a new kind of coupled boundary conditions. We transform the given system into an equivalent fixed point problem and solve it by applying the standard fixed point theorems. Examples are constructed for the illustration of the obtained results. [ABSTRACT FROM AUTHOR]